\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{amssymb} % \mathbb
\usepackage{graphicx}
\usepackage{tikz}
\usepackage{xcolor}

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\begin{document}

\begin{center}
{\LARGE Eigenmath Manual}

\bigskip
August 9, 2022
\end{center}

\tableofcontents

\newpage

\noindent
Eigenmath is available for both macOS and Linux.

\bigskip
\noindent
For macOS, commands are entered in the following field.

\begin{center}
\begin{tikzpicture}
\node at (0,0) {\includegraphics[scale=0.2]{screenshot.png}};
\draw[red,thick] (2.4,-2.1) ellipse (3.0cm and 0.5cm);
\end{tikzpicture}
\end{center}

\noindent
Multiple commands can be put together in a script.
Scripts are run by clicking the Run button.

\begin{center}
\begin{tikzpicture}
\node at (0,0) {\includegraphics[scale=0.2]{screenshot.png}};
\draw (-2.4,0.1) node {Scripts go here.};
\end{tikzpicture}
\end{center}

\noindent
After a script runs, all of the results are available in command mode.

\newpage

\input{nabokov}

\input{syntax}

\newpage

\subsection{Testing for equality}
The infix operator \verb$==$ is used to test for equality of operands.
The operator evaluates to 1 if the operands are equal and 0 if the operands are not equal.

{\color{blue}
\begin{verbatim}
exp(i pi) == -1
\end{verbatim}
}

\noindent
1

\bigskip
\noindent
The \verb$==$ operator uses \verb$simplify$ internally.
In effect, \verb$A==B$ is equivalent to \verb$simplify(A-B)==0$.

\input{arithmetic}

\input{exponents}

\input{symbols}

\input{complex}

\input{linear-algebra}

\subsection{Component arithmetic}

\noindent
Tensor plus scalar adds the scalar to each component of the tensor.

{\color{blue}
\begin{verbatim}
(x,y,z) + 10
\end{verbatim}
}

\noindent
$\displaystyle
\begin{bmatrix}
x+10
\\[1ex]
y+10
\\[1ex]
z+10
\end{bmatrix}
$

\bigskip
\noindent
The product of two tensors is the Hadamard (element-wise) product.

{\color{blue}
\begin{verbatim}
A = ((1,2),(3,4))
B = ((a,b),(c,d))
A B
\end{verbatim}
}

\noindent
$\displaystyle
\begin{bmatrix}
a & 2b
\\[1ex]
3c & 4d
\end{bmatrix}
$

\bigskip
\noindent
Tensor raised to a power raises each component to the power.

{\color{blue}
\begin{verbatim}
(x,y,z)^2
\end{verbatim}
}

\noindent
$\displaystyle
\begin{bmatrix}
x^2
\\[1ex]
y^2
\\[1ex]
z^2
\end{bmatrix}
$

\newpage

\input{derivative}

\input{integrals}

\input{integral-trick}

\input{line-integral}

\input{surface-area}

\input{surface-integral}

\input{greens-theorem}

\input{stokes-theorem}

\newpage

\section{Quantum Computing}

\input{quantum-computing}

\newpage

\section{Draw (macOS)}

\input{draw}

\newpage

\input{help}

\newpage

\input{tricks}

\end{document}
